How long to fill a air cylinder? Time vs. Pressure vs. Volume 2

[markdblissmn]

I am trying to figure out how to calculate how long it takes to fill an air storage tank of a certain size to a certain pressure given a compressor HP. What calculation or method should I use?

Imagine a 1000HP central facility compressor connected to a 4" main distribution line. If I have a 1000gallon air receiver and I want to fill it to 5atm pressure, how long would it take? How does the hose/pipe from the main 4in line affect it? How to size this hose? Cv factors like for liquids? Looking for guidance.

Thanks!

Mark Bliss

http://www.2RMengineering.com

 

[FredRosse]

Yes, a closed form solution may be had, and this is a more elegant solution.

In my experience getting a transient solution with many quasi-steady time steps is just as good as the more elegant solution we had to use 50 years ago without computers. With any PC we can simulate integration with small steps (as delta approaches zero, we have the integrated solution) to whatever practical result is required. Trying time steps at 1/10 the good solution, if it does not materially change the answer, then convergence is obtained. If not, then try smaller steps until the criteria is met. I know this method is somewhat "brute force computing", but it allows incorporating many other variables than you presented in your boundary conditions. For example, in perfect one dimensional flow, "choked flow" is well defined, however real gas systems behave somewhat differently (and hence the Y expansion factor for gas flow solution) and getting a closed form solution for this case would be quite a challenge without computer iteration.